Find all

Find all right-angled triangles whose side lengths form an arithmetic sequence.


n = (Correct answer is: ∞) Wrong answer

Step-by-step explanation:

a2+b2=c2 b=a+Δ c=b+Δ=a+2Δ  a2+(a+Δ)2=(a+2Δ)2 a22 aΔ3Δ2=0;a>0;Δ>0 (a3Δ)(a+Δ)=0;a>0;Δ>0 a3Δ=0;Δ>0 Δ=a/3  a=33 x b=34 x c=35 x;x>0  n=   Verifying Solution:  a1=3 b1=34 a1=34 3=34 3=312=4 c1=35 a1=35 3=35 3=315=5  a2=5 b2=34 a2=34 5=34 5=3206.6667 c2=35 a2=35 5=35 5=3258.3333  a3=10 b3=34 a3=34 10=34 10=34013.3333 c3=35 a3=35 10=35 10=35016.6667  n=

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Showing 1 comment:
Dr Math
there are infinity solutions. for leg lenght a,  difference AP is a/3. So right triangle has sides: a, a+a/3, a+2/3a

So all triangles are similar to triangle 3-4-5 and has length of sides: a ; 4/3 a ; 5/3*a

Tips for related online calculators
Are you looking for help with calculating roots of a quadratic equation?
Need help calculating sum, simplifying, or multiplying fractions? Try our fraction calculator.
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our right triangle calculator.
See also our trigonometric triangle calculator.

We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: